Categorical Approach to Swarm Computations

We propose the model approaching the problems of organisation, computing and emergent behavior of certain swarms from category theory point of view. In this model the Yoneda embedding to the category of presheaves spanned over the basic category of partial recursive functions, is activated by external stimuli and the resulting excited domains carry collective self-organising processes. We find that the intuitionistic logic of the presheaf topos becomes a primary logic for a way how swarms act and how they should be described algorithmically.

Automated summary

The proposed model addresses organizational, computational, and emergent behavior issues of certain swarms from the perspective of category theory. By activating the Yoneda embedding to the category of presheaves spanned over the basic category of partial recursive functions, external stimuli trigger excited domains that facilitate collective self-organizing processes. The intuitionistic logic of the presheaf topos is identified as the primary logic for understanding and algorithmically describing swarm behavior.